{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "from statsmodels.tsa.arima_model import ARMA\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perform_adf_test(series):\n",
    "    result = adfuller(series)\n",
    "    print('ADF Statistic: %f' % result[0])\n",
    "    print('p-value: %f' % result[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Original Series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ts = pd.read_csv('original_series.csv')\n",
    "ts.index = np.arange(1,len(ts)+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Views')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(ts)\n",
    "\n",
    "plt.xticks(np.arange(0,78,6), fontsize=14)\n",
    "plt.xlabel('Hours Since Published', fontsize=16)\n",
    "\n",
    "plt.yticks(np.arange(0,50000,10000), fontsize=14)\n",
    "plt.ylabel('Views', fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Original Series: $v_t$\n",
    "\n",
    "# (1) Normalize ($v_t \\rightarrow n_t$): $n_t = \\frac{v_t - \\mu}{\\sigma}$\n",
    "\n",
    "# (2) Exponentiate ($n_t \\rightarrow e_t$): $e_t = e^{n_t}$\n",
    "\n",
    "# (3) First Difference ($e_t \\rightarrow d_t$): $d_t = e_t - e_{t-1}$\n",
    "\n",
    "# $d_t = e^{\\frac{v_t - \\mu}{\\sigma}} - e^{\\frac{v_{t-1} - \\mu}{\\sigma}}$\n",
    "\n",
    "# ------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# (1) Normalize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = np.mean(ts).iloc[0]\n",
    "sigma = np.std(ts).iloc[0]\n",
    "\n",
    "norm_ts = (ts - mu) / sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x243588e5a08>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(norm_ts)\n",
    "\n",
    "plt.xticks(np.arange(0,78,6), fontsize=14)\n",
    "plt.xlabel('Hours Since Published', fontsize=16)\n",
    "\n",
    "plt.yticks(np.arange(-3,2), fontsize=14)\n",
    "plt.ylabel('Norm. Views', fontsize=16)\n",
    "\n",
    "plt.axhline(0, color='k', linestyle='--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# (2) Exponentiate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "exp_ts = np.exp(norm_ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Exp. Norm. Views')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(exp_ts)\n",
    "\n",
    "plt.xticks(np.arange(0,78,6), fontsize=14)\n",
    "plt.xlabel('Hours Since Published', fontsize=16)\n",
    "\n",
    "plt.yticks(np.arange(0,3.5,.5), fontsize=14)\n",
    "plt.ylabel('Exp. Norm. Views', fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: 1.648979\n",
      "p-value: 0.997997\n"
     ]
    }
   ],
   "source": [
    "perform_adf_test(exp_ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# (3) First Difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "diff_ts = exp_ts.diff().dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'First Diff. \\nExp. Norm. Views')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(diff_ts)\n",
    "\n",
    "plt.xticks(np.arange(0,78,6), fontsize=14)\n",
    "plt.xlabel('Hours Since Published', fontsize=16)\n",
    "\n",
    "plt.yticks(np.arange(-0.2,0.3,.1), fontsize=14)\n",
    "plt.ylabel('First Diff. \\nExp. Norm. Views', fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -4.881064\n",
      "p-value: 0.000038\n"
     ]
    }
   ],
   "source": [
    "perform_adf_test(diff_ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit AR Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pacf(diff_ts)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(diff_ts)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ritvik\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:214: ValueWarning: An unsupported index was provided and will be ignored when e.g. forecasting.\n",
      "  ' ignored when e.g. forecasting.', ValueWarning)\n"
     ]
    }
   ],
   "source": [
    "#create the model\n",
    "model = ARMA(diff_ts, order=(4,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_fit = model.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predict Out 3 Hours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction_info = model_fit.forecast(3)\n",
    "\n",
    "predictions = prediction_info[0]\n",
    "lower_bound = prediction_info[2][:,0]\n",
    "upper_bound = prediction_info[2][:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x24358a97488>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(diff_ts)\n",
    "\n",
    "plt.xticks(np.arange(0,78,6), fontsize=14)\n",
    "plt.xlabel('Hours Since Published', fontsize=16)\n",
    "\n",
    "plt.yticks(np.arange(-0.2,0.3,.1), fontsize=14)\n",
    "plt.ylabel('First Diff. \\nExp. Norm. Views', fontsize=16)\n",
    "\n",
    "plt.plot(np.arange(len(ts)+1, len(ts)+4), predictions, color='g')\n",
    "plt.fill_between(np.arange(len(ts)+1, len(ts)+4), lower_bound, upper_bound, color='g', alpha=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Undo Transformations: ($\\hat{d}_{t+1} \\rightarrow \\hat{v}_{t+1}$)\n",
    "\n",
    "# $\\hat{v}_{t+1} = \\sigma \\ln(\\hat{d}_{t+1} + e^{\\frac{v_t - \\mu}{\\sigma}}) + \\mu$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def undo_transformations(predictions, series, mu, sigma):\n",
    "    first_pred = sigma*np.log(predictions[0] + np.exp((series.iloc[-1]-mu)/sigma)) + mu\n",
    "    orig_predictions = [first_pred]\n",
    "    \n",
    "    for i in range(len(predictions[1:])):\n",
    "        next_pred = sigma*np.log(predictions[i+1] + np.exp((orig_predictions[-1]-mu)/sigma)) + mu\n",
    "        orig_predictions.append(next_pred)\n",
    "    \n",
    "    return np.array(orig_predictions).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "orig_preds = undo_transformations(predictions, ts, mu, sigma)\n",
    "orig_lower_bound = undo_transformations(lower_bound, ts, mu, sigma)\n",
    "orig_upper_bound = undo_transformations(upper_bound, ts, mu, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x24358cd7c08>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(ts)\n",
    "\n",
    "plt.xticks(np.arange(0,78,6), fontsize=14)\n",
    "plt.xlabel('Hours Since Published', fontsize=16)\n",
    "\n",
    "plt.yticks(np.arange(0,50000,10000), fontsize=14)\n",
    "plt.ylabel('Views', fontsize=16)\n",
    "\n",
    "plt.plot(np.arange(len(ts)+1, len(ts)+4), orig_preds, color='g')\n",
    "plt.fill_between(np.arange(len(ts)+1, len(ts)+4), orig_lower_bound, orig_upper_bound, color='g', alpha=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(40000.0, 45000.0)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(ts)\n",
    "\n",
    "plt.xticks(np.arange(0,78), fontsize=14)\n",
    "plt.xlabel('Hours Since Published', fontsize=16)\n",
    "\n",
    "plt.yticks(np.arange(40000,46000,1000), fontsize=14)\n",
    "plt.ylabel('Views', fontsize=16)\n",
    "\n",
    "plt.plot(np.arange(len(ts)+1, len(ts)+4), orig_preds, color='g')\n",
    "plt.fill_between(np.arange(len(ts)+1, len(ts)+4), orig_lower_bound, orig_upper_bound, color='g', alpha=0.1)\n",
    "plt.xlim(64,76)\n",
    "plt.ylim(40000, 45000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
